{"paper":{"title":"Local and Non-Local Dirichlet Forms on the Sierpi\\'nski Gasket and the Sierpi\\'nski Carpet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Meng Yang","submitted_at":"2019-01-21T12:07:25Z","abstract_excerpt":"This thesis is about local and non-local Dirichlet forms on the Sierpi\\'nski gasket and the Sierpi\\'nski carpet. We are concerned with the following three problems in analysis on the Sierpi\\'nski gasket and the Sierpi\\'nski carpet.\n  First, a unified purely \\emph{analytic} construction of local regular Dirichlet forms on the Sierpi\\'n-ski gasket and the Sierpi\\'nski carpet. We give a purely analytic construction of a self-similar local regular Dirichlet form on the Sierpi\\'nski carpet using $\\Gamma$-convergence of stable-like non-local closed forms which gives an answer to an open problem in a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06897","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}